A226801 Column 6 of array in A226513.

4683, 25988, 87135, 227304, 507035, 1014348, 1871583, 3242960, 5342859, 8444820, 12891263, 19103928, 27595035, 38979164, 53985855, 73472928, 98440523, 130045860, 169618719, 218677640, 278946843, 352373868, 441147935, 547719024, 674817675, 825475508

Offset

0,1

Comments

This is the case h = 6 in Sum_{k=0..h} S2(h,k)*k!*binomial(n+k,k), where S2 is the Stirling number of the second kind (see the Ahlbach et al. paper, Theorem 3). [Bruno Berselli, Jun 20 2013]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Connor Ahlbach, Jeremy Usatine and Nicholas Pippenger, Barred Preferential Arrangements, Electron. J. Combin., Volume 20, Issue 2 (2013), #P55.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (4683 - 6793*x + 3562*x^2 - 798*x^3 + 67*x^4 - x^5) / (1-x)^7.

a(n) = (n + 1)*(n^5 + 35*n^4 + 430*n^3 + 2320*n^2 + 5525*n + 4683).

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

E.g.f.: exp(x)*(4683 + 21305*x + 19921*x^2 + 6530*x^3 + 890*x^4 + 51*x^5 + x^6). - Franck Maminirina Ramaharo, Nov 29 2018

Mathematica

Table[(n + 1) (n^5 + 35 n^4 + 430 n^3 + 2320 n^2 + 5525 n + 4683), {n, 0, 40}] (* or *) CoefficientList[Series[(4683 - 6793 x + 3562 x^2 - 798 x^3 + 67 x^4 - x^5) / (1-x)^7, {x, 0, 30}], x]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {4683, 25988, 87135, 227304, 507035, 1014348, 1871583}, 30] (* Harvey P. Dale, Apr 27 2014 *)

Prog

(Magma) [(n+1)*(n^5+35*n^4+430*n^3+2320*n^2+5525*n+4683): n in [0..35]]; /* or */ I:=[4683, 25988, 87135, 227304, 507035, 1014348, 1871583]; [n le 7 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..30]];

Crossrefs

Cf. columns 2, 3, 4, 5 of A226513: A005563, A226514, A226741, A226800.

Sequence in context: A022244 A252382 A190131 * A320620 A218096 A293583

Adjacent sequences: A226798 A226799 A226800 * A226802 A226803 A226804

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 20 2013

Status

approved